References of "Lejeune, Marie"
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See detailComputing the k-binomial complexity of the Tribonacci word
Lejeune, Marie ULiege

Scientific conference (2019, April 03)

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See detailTemplates for the k-binomial complexity of the Tribonacci word
Lejeune, Marie ULiege; Rigo, Michel ULiege; Rosenfeld, Matthieu ULiege

E-print/Working paper (2019)

Consider the k-binomial equivalence: two finite words are equivalent if they share the same subwords of length at most k with the same multiplicities. With this relation, the k-binomial complexity of an ... [more ▼]

Consider the k-binomial equivalence: two finite words are equivalent if they share the same subwords of length at most k with the same multiplicities. With this relation, the k-binomial complexity of an infinite word x maps the integer n to the number of pairwise non-equivalent factors of length n occurring in x. In this paper based on the notion of template introduced by Currie et al., we show that, for all k > 1, the k-binomial complexity of the Tribonacci word coincides with its usual factor complexity p(n)=2n+1. A similar result was already known for Sturmian words but the proof relies on completely different techniques that seemingly could not be applied for Tribonacci. [less ▲]

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See detailAbout the k-binomial equivalence and the associated complexity
Lejeune, Marie ULiege

Conference (2019, March 07)

In these slides, we present the notions of k-binomial equivalence, and k-binomial complexity. For an arbitrary infinite word w, this function maps every non-negative integer n to the number of length-n ... [more ▼]

In these slides, we present the notions of k-binomial equivalence, and k-binomial complexity. For an arbitrary infinite word w, this function maps every non-negative integer n to the number of length-n factors in w. We then study the values of this function on several well-known infinite words. We finally discuss more deeply the notion of k-binomial equivalence and we rise some interesting open questions. [less ▲]

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See detailComputing the k-binomial complexity of the Thue-Morse word
Lejeune, Marie ULiege

Scientific conference (2019, January 17)

The goal of this presentation was to present the tools used to compute the exact value of the k-binomial complexity of the Thue-Morse word.

Detailed reference viewed: 12 (4 ULiège)
See detailComputing the k-binomial complexity of the Thue–Morse word
Lejeune, Marie ULiege; Leroy, Julien ULiege; Rigo, Michel ULiege

E-print/Working paper (2018)

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See detailCalculer la complexité k-binomiale du mot de Thue-Morse
Lejeune, Marie ULiege

Scientific conference (2018, December 06)

The goal of the presentation was to present the tools used to compute the exact value of the k-binomial complexity of the Thue-Morse word.

Detailed reference viewed: 11 (4 ULiège)